Thanks for the tips. I was able to eject and get rid of Flash and Logmein, but Skype seems to persist. When I try to remove or eject it I get a message saying it is in use. I force quit Skype and then was able to remove it but when I reopened Skype it came back. Perhaps I am doing something wrong with the Skype install.
It does appear to be running from the disk image even though I dragged it to the applications folder. If I close it all down and then reopen Skype, I get a message saying it is downloaded from the Internet and do I still want to use it. When I say yes then it puts that disk image back on the desktop.
How do I get it to run as a simple app?